Exponential and Logarithmic Functions Overview — AP Precalculus
1. Unit at a Glance
This unit starts by building on your understanding of sequences and linear functions to contrast constant additive change (linear/arithmetic) with constant multiplicative change (exponential/geometric). We then move to core foundational function concepts: composition and inverse functions, which set up the formal definition of logarithms as the inverse of exponential functions.
After building core definitions of exponential and logarithmic functions, you will learn to manipulate expressions, solve equations and inequalities, and apply these functions to model real-world data, including using semi-log plots to linearize exponential data. The learning arc flows from foundational definitions to manipulation, problem solving, and applied modeling.
Common Pitfalls
Why: Students often mix up constant additive change (linear) and constant multiplicative change (exponential).
Why: Logarithms only accept positive arguments, so solutions that produce negative arguments are invalid.
Why: Students often incorrectly expand $\ ext{log}_b(a + c)$ to $\ ext{log}_b a + \\text{log}_b c$.